1. Field of the Invention
The present invention relates to data coding and decoding and, more particularly, to systems and methods for forward error correction (FEC) coding and decoding to enable delivery of large digital files reliably to many remote sites at high speeds.
2. Description of Related Art
Today, the availability of powerful digital computational tools has yielded the ability to present information in forms that go far beyond text and numbers. There now exists the capability to create and share data in more complex multimedia forms, using graphics, audio, still images and moving images (video), as well as combinations of those forms. Such data may be transferred from a host device, such as a host computer, to a potentially large number of subscriber devices, such as radio, television, mobile telephone, and computer devices.
One technique for transferring data is to broadcast it using one-way broadcasting systems such as satellite broadcasting systems. One notable drawback of one-way satellite broadcast systems, however, as compared to some other methods of information distribution such as computer networks, is the inability of the subscriber devices to inform the host device that a reception error has occurred. Thus, it is essential that the transferred data be transferred in such a way that all of the subscriber devices can recover from reception errors to avoid such problems.
The above drawback of one-way broadcasting (e.g., satellite broadcasting) is further compounded by the greater vulnerability of the broadcast signal to various forms of noise interference present in the transmission channel. One form of noise that is always present in the communications channel is “white” noise. For example, white noise is introduced in the channel by the thermal radiation of the gaseous constituents of the earth's surface. The strength and frequency of this noise varies, and it sometimes overpowers the transmitted signal causing it to be received erroneously. Because of white noise, a transmitted binary “zero” bit is occasionally received erroneously as a binary “one” bit, and vice-versa. Such errors are known as bit errors. White noise generally tends to cause isolated bit errors in a transmitted message. Although these bit errors are usually spread out throughout the message, they can be easily detected and corrected, because they are isolated.
In contrast with white noise, “impulse” noise tends to wipe out long sequences of consecutive bits. Such errors are known as “burst” errors. Their duration varies from a few milliseconds to a few seconds, but certain phenomena, such as rainstorms or sunspots, can cause burst errors of even longer duration such as a few minutes. Unlike bit errors due to white noise, burst errors are not distributed over the entire message, but only a portion thereof. However, burst errors are more difficult to detect and correct, because they wipe out so many consecutive bits of data.
Well-known error detection and correction (EDAC) schemes are used to reduce the effects of errors caused by white noise. EDAC schemes generally operate at the bit level by adding enough redundant data bits to the data to detect and correct the received data. In practice, EDAC schemes can only detect and correct a limited amount of bit errors. The redundant data added to the original data, however, obviously increases the amount of data to be transmitted and thus the transmission bandwidth and transmission time. Well-known EDAC schemes include Hamming, Viturbi, Reed-Solomon, and other forward error correction (FEC) coding schemes.
Interleaving may also be performed at the bit level. Interleaving rearranges the data bits so that they are non-sequentially transmitted. The subscriber device deinterleaves the received bits to reorder the bits as they originally appeared. This technique reduces the effect of errors in a sequence of bits. Although interleaving does not in itself correct those bit errors, by non-sequentially reordering the data bits in a block of data that is to be transmitted by the host device, the bit errors are more uniformly distributed over the received block of data upon deinterleaving by the subscriber device. By isolating the bit errors, interleaving enhances bit-level EDAC coding performance. Both EDAC and interleaving can also be performed on data symbols representing groups of bits, such as bytes.
In most broadcast systems, the transmitted data bits or symbols are most likely to be organized into large groups called packets, and a large data file is transmitted as a sequence of packets. The addressed subscriber devices reconstruct the large data file from the received packets. The above-described noise bursts can typically damage one or more long sequences of consecutive packets. Those packets are either not received by one or more of the subscriber devices or are received severely corrupted. Although bit-level EDAC schemes might be able to correct some of the corrupted packets, depending on the number of erroneous bits in those corrupted packets, these schemes are simply not robust enough to correct the great majority of those corrupted packets. This is because, in extended periods of burst noise, a large amount of both the original data bits and redundant EDAC bits in a packet are received corrupted, thus making bit-level error correction, and thus packet-level error-correction, impossible. Moreover, EDAC schemes are useless in the case of those packets not received.
One known method for reducing the effect of burst errors in such broadcast systems is retransmission of those packets that were not received or were received corrupted and could not be corrected (hereinafter those packets are simply referred to as “lost”). For example, a host device may broadcast via satellite to two geographically widely-separated subscriber devices A and B. Due to this wide separation, subscriber device A and subscriber device B may experience different weather conditions, and thus different patterns of noise. For example, subscriber device A may lose 20% of the transmitted packets, while subscriber computer B may successfully receive all the transmitted packets. Although it is possible to rebroadcast an entire file of data to all the subscriber devices, current methods of doing this are costly, waste time and bandwidth, and prevent communications channels from being used for other purposes. In the above example, subscriber device A would identify the lost packets (by examining the serial numbers of the correctly received packets) and would ask the host device to retransmit the packets it missed until the entire large data file could be reconstructed perfectly by subscriber computer A. In the satellite broadcast example given above, the request for missed packet retransmission is made through a back channel, and the host device rebroadcasts those missed packets via the satellite. Alternatively, the host device retransmits those missed packets only to subscriber device A through the back channel.
Retransmission of lost packets requires, however, (1) two-way communication back channels from all of the subscriber devices to the host device so each subscriber computer can inform the host device of which packets were lost, and (2) a retransmission protocol between the host device and the subscriber devices. Each back channel usually takes the form of a modem and telephone lines, or is part of a standard computer network. The back channel therefore has a limited bandwidth and can timely transmit only a limited amount of information. Back channels are also expensive. Further, retransmission increases the time required to distribute the data, and prevents the host device and subscriber devices from doing other tasks. In some applications, such as a mobile receiver, use of back channels may simply be impossible.
There have been some attempts to overcome these disadvantages. For example, low density parity-check codes, which use a randomized encoding matrix, have been used. As will be explained below, the codes used in the method of the present invention are generally not low density. Further, for decoding, as will also be shown below, the present invention uses Gaussian elimination rather than a potentially more efficient belief propagation that requires a low density assumption. In addition, Digital Fountain, Inc. has used codes which are said to address the burst-mode error channel discussed above. However, those codes, unlike the codes of the present invention as discussed below, are sparse.
The ability to communicate reliably is fundamental to any communications scheme. Therefore, it is desirable to provide a method and system for correction coding and decoding that overcomes the disadvantages noted above. There is also a need for a scheme for generating from a finite set of data an unbounded number of packets for transmission to a receiver, out of which any sufficiently large subset of those packets is sufficient to reconstruct an original source file.